A method for realization of an ARMAX lattice filter

This paper proposes a method for realization of an ARMAS lattice filter. The ARMAX (autoregressive moving average model with exogenous variable) model identification is significant because the ARMAX model is a standard tool in the control field, and it can be performed by the proposed algorithm. One of the recursive least-square methods for the ARMAX model identification is the ELS (extended least squares). Applied to the ARMAX model identification, the ELS uses o(N²) multiplications, where NΔ=AR order+MA order+X order. When the proposed realization method of the ARMAX lattice filter is used, o(M) multiplications are needed for the ARMAX model identification, where MΔ=max{AR, order, MA order, X order}